Symmetry-based matrix factorization

AbstractWe present a method for factoring a given matrix M into a short product of sparse matrices, provided that M has a suitable “symmetry”. This sparse factorization represents a fast algorithm for the matrix–vector multiplication with M. The factorization method consists of two essential steps. First, a combinatorial search is used to compute a suitable symmetry of M in the form of a pair of group representations. Second, the group representations are decomposed stepwise, which yields factorized decomposition matrices and determines a sparse factorization of M. The focus of this article is the first step, finding the symmetries. All algorithms described have been implemented in the library AREP. We present examples for automatically generated sparse factorizations—and hence fast algorithms—for a class of matrices corresponding to digital signal processing transforms including the discrete Fourier, cosine, Hartley, and Haar transforms

Rotational Stiffness of Timber-to-Timber Connections with Self-Tapping axially loaded Screws

Self-tapping axially loaded screws provide high load-carrying capacity and great stiffness. Due to these advantages, they were preferably applied to realise connections for tension members. While the translational stiffness of those connections can be estimated for engineering purposes sufficiently, knowledge about the rotational stiffness is still low. The investigations reported here show the influence of the inclination and the geometrical arrangement of the self-tapping screws on the rotational stiffness of connections for tension members. A test set-up was therefore developed. It enables that tensile forces and rotation are simultaneously effective and quantitatively independently of each other. The experimental results show that the inclination of the screws and the resulting compressive stress in the shear plane has a major influence on the rotational stiffness and that the stiffness of the screws themselves becomes less effective

Entropy of a bit-shift channel

We consider a simple transformation (coding) of an iid source called a bit-shift channel. This simple transformation occurs naturally in magnetic or optical data storage. The resulting process is not Markov of any order. We discuss methods of computing the entropy of the transformed process, and study some of its properties.Comment: Published at http://dx.doi.org/10.1214/074921706000000293 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Multi-Conjugate Adaptive Optics for LINC-NIRVANA : Laboratory Tests of a Ground-Layer Adaptive Optics System and Virtical Turbulence Measurements at Mt. Graham

Turbulence in Earth's atmosphere severely limits the image quality of ground-based telescopes. With the technique of Adaptive Optics, the induced distortions of the light can be measured and corrected in real-time, regaining nearly diffraction-limited performance. Unfortunately, when using a single guide star to measure the distortions, the correction is only useful within a small angular area centered on the guide star. The first part of this thesis presents a laboratory setup, which uses four guide stars to measure the turbulence-induced distortions and one deformable mirror to correct the most turbulent layer. With such a Layer-Oriented Ground-Layer Adaptive Optics (GLAO) system, the area of useful correction is significantly increased. The system is characterized in static and dynamic operation, and the influence of non-conjugated turbulent layers, the effect of brightness variations of the guide-stars and the impact of misalignments are studied. Furthermore, calibration strategies and the performance of the Kalman control algorithm are examined. The second part of this thesis focuses on SCIDAR measurements of the atmospheric turbulence above Mt. Graham. This dataset provides for the first time a statistical and thorough analysis of the vertical turbulence structure above the LBT site. Based on 16 nights of measurements, spread over one year, Mt. Graham appears to be an excellent site for an astronomical observatory. By extending an analytical model, describing the filtering of the turbulence-induced distortions by an AO system, we calculate performance expectations of the LINC-NIRVANA instrument. In particular, the optimal conjugation heights of the deformable mirrors are studied. Furthermore, we present a new method to measure the atmospheric turbulence near the ground with 40 times increased vertical resolution, compared to standard SCIDAR. First on-sky results demonstrate the power of this technique

Polynomial time algorithms for multicast network code construction

The famous max-flow min-cut theorem states that a source node s can send information through a network (V, E) to a sink node t at a rate determined by the min-cut separating s and t. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to re-encode the information they receive. We demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed. We give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity. We extend these algorithms to integer capacities and to codes that are tolerant to edge failures

PSF reconstruction for NAOS-CONICA

Adaptive optics (AO) allows one to derive the point spread function (PSF) simultaneously to the science image, which is a major advantage in post-processing tasks such as astrometry/photometry or deconvolution. Based on the algorithm of \citet{veran97}, PSF reconstruction has been developed for four different AO systems so far: PUEO, ALFA, Lick-AO and Altair. A similar effort is undertaken for NAOS/VLT in a collaboration between the group PHASE (Onera and Observatoire de Paris/LESIA) and ESO. In this paper, we first introduce two new algorithms that prevent the use of the so-called "$U\_{ij}$ functions" to: (1) avoid the storage of a large amount of data (for both new algorithms), (2) shorten the PSF reconstruction computation time (for one of the two) and (3) provide an estimation of the PSF variability (for the other one). We then identify and explain issues in the exploitation of real-time Shack-Hartmann (SH) data for PSF reconstruction, emphasising the large impact of thresholding in the accuracy of the phase residual estimation. Finally, we present the data provided by the NAOS real-time computer (RTC) to reconstruct PSF ({\em (1)} the data presently available, {\em (2)} two NAOS software modifications that would provide new data to increase the accuracy of the PSF reconstruction and {\em (3)} the tests of these modifications) and the PSF reconstruction algorithms we are developing for NAOS on that basis.Comment: 12 pages & 13 figures. To be published in the proceedings of the SPIE conference Advances in Adaptive Optics - Astronomical Telescopes & Instrumentation, 24-31 May 2006, Orland

Search for Outer Massive Bodies around Transiting Planetary Systems: Candidates of Faint Stellar Companions around HAT-P-7

We present results of direct imaging observations for HAT-P-7 taken with the Subaru HiCIAO and the Calar Alto AstraLux. Since the close-in transiting planet HAT-P-7b was reported to have a highly tilted orbit, massive bodies such as giant planets, brown dwarfs, or a binary star are expected to exist in the outer region of this system. We show that there are indeed two candidates for distant faint stellar companions around HAT-P-7. We discuss possible roles played by such companions on the orbital evolution of HAT-P-7b. We conclude that as there is a third body in the system as reported by Winn et al. (2009, ApJL, 763, L99), the Kozai migration is less likely while planet-planet scattering is possible.Comment: 8 pages, 3 figures, 2 tables, PASJ in pres